Cohen notified U.S. District Court in Los Angeles on Thursday he intends to request a stay in Daniels' lawsuit against him and Trump "on the grounds that an ongoing criminal investigation overlaps with the facts of this case," a reference to the possibility that his testimony could be used by prosecutors to build a related criminal case against Cohen.

Cohen, who has denied wrongdoing, has been at the center of a controversy surrounding a $130,000 payment to Daniels, whose real name is Stephanie Clifford. She has alleged that she had sex once in 2006 with Trump and was paid shortly before the 2016 election to keep quiet about it. Daniels claims Cohen's denials portray her as a liar and sued for defamation.

The Federal Bureau of Investigation raided Cohen's offices and home on Monday as part of a probe into possible bank and tax fraud and possible campaign law violation connected to the payment, a source familiar with the investigation told Reuters. [nL1N1RM1R7]

In the defamation-case filing, Cohen raised the possibility of invoking his constitutional right under the Fifth Amendment against self-incrimination if the stay is not granted, which would allow him to refuse to testify.

Michael Avenatti, lawyer for Stormy Daniels told Reuters that Cohen's attorney told him that Cohen will plead the Fifth if his application for a stay is denied.

Cohen's attorney Brent Blakely said, "No decision has been made for Mr. Cohen to assert his Fifth Amendment rights."

"It is common for a civil case to be stayed under these circumstances, and that is what we will be requesting of the U.S. District Court tomorrow," Blakely said in an email.

The judge in the suit has given Cohen until Friday evening to formally request the stay.

Daniels has until Monday evening to file her opposition, and then Cohen will have through Tuesday evening to respond to her.